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Deep Learning in Finance

In their study, researchers of the School of Business and Economics have shown that algorithms based on artificial intelligence are able to make profitable investment decisions. When applied to the S&P 500 constituents from 1992 to 2015, their stock selections generated annual returns in the double digits – whereas the highest profits were made at times of financial turmoil. The findings have recently been published in the European Journal of Operational Research (EJOR) – a leading outlet in the field of operational research and decision making.*

In March 2016 Lee Sedol – one of the best human players in the Asian board game Go – lost against AlphaGo, a software developed by Google DeepMind. Compared to chess, Go is much more complex, and has long been considered an Everest for artificial intelligence research. Driving force for such achievements are computer programs that are loosely inspired by how biological brains work, i.e., by learning from examples and independently extracting relationships from millions of data points. “Artificial neural networks are primarily applied to problems, where solutions cannot be formulated with explicit rules”, explains Dr. Christopher Krauss (Chair of Statistics and Econometrics, FAU). “Image and speech recognition are typical fields of application, such as Apple’s Siri. But the relevance of deep learning also increases in other domains, such as weather forecasting or the prediction of economic developments.”

Analyzing capital market data

The international team around Dr. Christopher Krauss – composed of Xuan Anh Do (FAU) and Nicolas Huck (ICN Business School, France) – were the first academics to apply a selection of state-of-the-art techniques of artificial intelligence research to a large-scale set of capital market data. “Equity markets exhibit complex, often non-linear dependencies,” says Dr. Krauss. “However, when it comes to selecting stocks, established methods are mainly modeling simple relationships. For example, the momentum effect only focuses on a stock’s return over the past months and assumes a continuation of that performance in the months to come. We saw potential for improvements.” To find out whether machine learning approaches perform better than a naïve buy-and-hold strategy, Dr. Krauss’s group studied the S&P 500 index, consisting of the 500 leading U.S. stocks. For the period from 1992 to 2015, they generated predictions for each individual stock for every single trading day, leveraging deep learning, gradient boosting, and random forests.

Outperformance with machine learning

Each of these methods was trained with approximately 180 million data points. In the course of this training, the models learn a complex function, describing the relationship between price-based features and a stock’s future performance. The results are astonishing: “Since the year 2000, we observe statistically and economically significant returns of more than 30% per annum. In the nineties, results were even higher, reflecting a time when our machine learning approaches had not yet been invented”, explains Dr. Krauss. These results pose a serious challenge to the efficient-market hypothesis. Returns are particularly high during times of financial turmoil, e.g., the collapse of the dot-com bubble around the year 2000 or the global financial crisis in 2008/2009. Dr. Krauss: “Our quantitative algorithms have turned out to be particularly effective at such times of high volatility, when emotions are dominating the markets.”

Deep learning still has potential

However, Dr. Krauss lowers expectations: “During the last years of our sample period, profitability decreased and even became negative at times. We assume that this decline was driven by the rising influence of artificial intelligence in modern trading – enabled by increasing computing power as well as by the popularization of machine learning.” However, the researchers agree that deep learning still has significant potential: “Currently, we are working on promising follow-up projects with far larger data sets and very deep network architectures that have been specifically designed for identifying temporal dependencies”, says Dr. Krauss. “First results already show significant improvements of predictional accuracy – also in recent years.”

The results of the study were published under the title “Deep neural networks, gradient-boosted trees, random forests: Statistical arbitrage on the S&P 500” in the European Journal of Operational Research.